The suitable interpolation between classical percolation and a special variant of explosive percolation enables the explicit realization of a tricritical percolation point. With high-precision simulations of the order parameter and the second moment
of the cluster size distribution a fully consistent tricritical scaling scenario emerges yielding the tricritical crossover exponent $1/phi_t=1.8pm0.1$.
We introduce a new Forward-Flux Sampling in Time (FFST) algorithm to efficiently measure transition times in rare-event processes in non-equilibrium systems, and apply it to study the first-order (discontinuous) kinetic transition in the Ziff-Gulari-
Barshad model of catalytic surface reaction. The average time for the transition to take place, as well as both the spinodal and transition points, are clearly found by this method.
In many dynamical systems there is a large separation of time scales between typical events and rare events which can be the cases of interest. Rare-event rates are quite difficult to compute numerically, but they are of considerable practical import
ance in many fields: for example transition times in chemical physics and extinction times in epidemiology can be very long, but are quite important. We present a very fast numerical technique that can be used to find long transition times (very small rates) in low-dimensional systems, even if they lack detailed balance. We illustrate the method for a bistable non-equilibrium system introduced by Maier and Stein and a two-dimensional (in parameter space) epidemiology model.
